Internally 4-connected binary matroids with cyclically sequential orderings

We characterize all internally 4-connected binary matroids M with the property that the ground set of M can be ordered ( e 0 , … , e n − 1 ) in such a way that { e i , … , e i + t } is 4-separating for all 0 ≤ i , t ≤ n − 1 (all subscripts are read modulo  n ). We prove that in this case either n ≤ 7 or, up to duality, M is isomorphic to the polygon matroid of a cubic or quartic planar ladder, the polygon matroid of a cubic or quartic Möbius ladder, a particular single-element extension of a wheel, or a particular single-element extension of the bond matroid of a cubic ladder.